A Study on The Pattern Generator by Using Complex System Methods

本研究课题是基于复杂系统方法的模式发生器的研制。由于在生成器中引入了随机决策过程，因此生成的模式是一个具有半自然形式和无限变化的抽象模式。因此，我们在本报告中称这一过程为偶然过程。该生成器的特点是模拟任意过程，生成任意形状。随机过程的基本思想是：假设过程可以用函数表示，函数中有涌现因子，每个因子用子因子表示，每个子因子有决策过程，如果在过程中引入随机决策，则因子之间有无穷多个组合;在整个过程中产生了数以百万计的变化，因此结果是不可预测的;也就是说，变化导致了一个偶然的过程。因此，该方法适用于各种不可预测的可视环境的建模。在这份报告中，我们介绍了层次选择性决策表示的出现因素及其子因素。我们首先讨论涌现因子的数学定义。然后阐明了任意形式的生成问题。其次，介绍了该方法在复杂系统方法（元胞自动机和混沌）生成任意形状中的应用。然后在该方法中引入了缩放、旋转、剪切和对称变换等变换函数。在此基础上，开发了任意形状生成的计算程序，并将其应用于形状生成。最后，我们将生成的形式应用到艺术和视觉设计作品中。

This research project has been done for the development of a pattern generator based on complex system methods. Since random decision processes are introduced into the generator, a generated pattern is an abstract one which has a semi-natural form and has an infinite variation. Thus we call the process an aleatory process in this report. The characteristics of the generator is to simulate an aleatory process and to generate an aleatory form. The basic idea of an aleatory process is as follows : Suppose a process can be expressed by some functions, the functions have emergence factors, each factor is represented by sub-factors, and each sub-factor has decision processes ; If we introduce random decisions in the processes, then an infinite number of combinations among factors occur ; And millions of variations are produced in the total process and thus resultants are unpredictable ; Namely, the variations cause an aleatory process. As a consequence the method is applicable to the modeling of various unpredictable visible environment.In this report, we introduce hierarchical selective decisions for representing the emergence factors and its sub-factors. We first discuss the mathematical definition of the emergence factors. And then the problem for the generation of an aleatory form is clarified. Next, the application of the method to the generation of aleatory forms by the complex system methods (cellular automata and chaos) is presented. Then the transformation function such as scaling, rotation, shearing, and symmetrical transformations are introduced in this method. Following this, computing programs for the generation of aleatory forms are developed and applied to the form generation. And finally, we apply the generated forms to the arts and visual design works.